Preheat oven to 350F/180C.
Heat a large dutch oven over medium-high heat. Add 1 tbs of the oil and let it heat. Pat the short ribs dry with paper towels.
Brown the short ribs on all sides. This should be done in shifts--don't overcrowd the pan.
Remove to a plate. Add the remaining tablespoon of oil and repeat browning and remove remaining ribs to the plate.
Add the celery, carrot, onion and garlic. Cook for 1-2 minutes, stirring frequently.
Next add the tomato paste and stir into the veggies in the pot. Cook for about 1 minute.
Add the brown sugar, bay leaf, thyme, entire can of tomatoes, wine and chicken stock. Stir to combine.
Add the short ribs back to the pan. Cover tightly and bake for approximately 3 hours (or until meat is very tender).